Is there actually a security system in? On my Mom's Corolla, she has a security light that blinks, even though there isn't really a much of (if any) a security device installed. My mom thinks its for show to scare off potential intruders since the light blinks in a very visible way from the driver's window, even if the doors aren't locked.
If your Mom's Corolla is a 2005 or later, that light isn't for show, and the car does have a security device on it. The key is encrypted, and that light indicates the status of the system. Off= disarmed, blinking= armed and steady means initializing or malfunction depending on whether it is on steady when you are starting the car or if it goes on steady and stays on all the time. Steady while starting is fine, other wise, they system isn't working.
The encryption means that the car has to have the encrypted keys in order to start. Trying to hot wire the car is pointless, because no matter what wires you cross, the fuel pump isn't pumping unless that encrypted key is present in the ignition switch.
The blinking light also serves as a break in deterrent, statistics prove that cars with visible security indicators such as blinking lights and stickers are less likely to be broken into, regardless if they have such a system or not.